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We give simple examples of Kazhdan groups with infinite outer automorphismgroups. This answers a question of Paulin, independently answered by Ollivierand Wise by completely different methods. As arithmetic lattices in(non-semisimple) Lie groups, our examples are in addition finitely presented.  We also use results of Abels about compact presentability of p-adic groups toexhibit a finitely presented non-Hopfian Kazhdan group. This answers a questionof Ollivier and Wise.Comment: 9 pages, no figure. v4: statement of Theorem 3.1 correcte

Finitely presentable, non-Hopfian groups with Kazhdan's Property~(T) and infinite outer automorphism group